Thereof, can I work for US company from Europe?
As several others have said, the answer is yes, but with a few caveats. Most European countries have freelancer visas or long-stay visas for people whose income comes from outside the country.
Similarly, can you legally work remotely in another country? Yes, You Can Work Remotely From a Different Country
Yes, in many countries, US citizens will be able to carry out domestic business activities and thus stay in a country for “business purposes” for up to 90 days. Therefore, you do not need a business visa to carry out your domestic professional activities while abroad.
Just so, can I work for a US company remotely while I'm abroad?
Income is sourced based on where the work is performed. Thus, you do not need any visa nor work authorization to work for a US-company performing work while physically outside the United States. However, a U.S. company employing you remotely would become an employer in the jurisdiction(s) where you are performing work.
Can you work for a US company from another country?
In Summary: The U.S. Labor Department, the IRS, the SBA, and U.S. Immigration lawyers all say it is legal for a U.S. company (or any U.S. employer) to hire foreigners living outside of the U.S. as remote or telecommute workers.
